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Can a stationary dependent variable be a nonstationary variable?
Models for stationary dependent variables should not have nonstationary explanatory variables (except perhaps for stationary combinations of cointegrated nonstationary variables); otherwise the linear combination of the regressors would diverge from the regressand.
What does stationarity mean in time series regression?
Stationarity implies mean reversion: that the variable reverts toward a fixed mean after any shock
How to use VAR in a time series?
If (A) then first-difference each of the three variables ( x 1, x 2, x 3 ), and use them together with the stationary variable x 4 to build a VAR model. x 4 depends on the error correction term and lags of Δ x 1, Δ x 2, Δ x 3, x 4. x 4 depends on the error correction term and lags of Δ x 1, Δ x 2, Δ x 3, x 4.
Which is better a VaR or a VECM model?
In practice, it depends on the power of cointegration tests: If your variables are cointegrated and you used a VAR model: you could have done better by estimating a VECM model. Your estimations are still consistent (in fact superconsistent), but inefficient.
How is the VAR model useful for forecasting?
The VAR model has proven to be especially useful for describing the dynamic behavior of economic and financial time series and for forecasting. It often provides superior forecasts to those from univari- ate time series models and elaborate theory-based simultaneous equations models.
How to test the nonstationary series for cointegration?
Test each pair of the nonstationary series ( x 1 and x 2; x 1 and x 3; x 2 and x 3) for cointegration using the Johansen or the Engle-Granger test. Then test all three series ( x 1, x 2, x 3) for cointegration using the Johansen test. In general, you want the following:
What do you call three nonstationary series and one stationary series?
So you have three nonstationary series and one stationary series. Let us call them x 1, x 2, x 3, and x 4, respectively. Suppose the nonstationarity of x 1, x 2, x 3 is of a unit-root kind (rather than of some other kind); that is, each of x 1, x 2, x 3 is integrated of order one, I (1).